Question: Antonio's toy boat is bobbing in the water under a dock. The vertical distance $H$ (in $\text{cm}$ ) between the dock and the top of the boat's mast $t$ seconds after its first peak is modeled by the following function. Here, $t$ is entered in radians. $H(t) = {5}\cos\left({\dfrac{2\pi}{3}}t\right) - {35.5}$ How long does it take the toy boat to bob down from its peak to a height of $-35\text{ cm}$ ? Round your final answer to the nearest tenth of a second.
Explanation: Converting the problem into mathematical terms $H(t) = {5}\cos\left({{\dfrac{2\pi}{3}}}t\right) - {35.5}$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{3}}}=3$ seconds. We want to find the first solution to the equation $H(t)=-35$ within the period $0<t<3$. The answer The equation's two solutions within the desired period (rounded to the nearest tenth of a second) are $0.7$ and $2.7$. Therefore, it takes about $0.7$ seconds for the boat to bob down to $-35\text{ cm}$.